How Undergraduates Compute Pure Nash Equilibria in Strategic Games
نویسنده
چکیده
In 2x2 games we often solve them by writing arrows between outcomes in the matrix. I make this procedure precise and generalize it to all strategic games using some very basic category theory. I define a strategic game in categorical form in which outcomes are objects and preferences are arrows. A subcategory is formed by exclusion of arrows between outcomes that can not be reached unilaterally. I show that Nash equilibria in pure strategies are never in the domain of non-isomorphisms of the subcategory, i.e. a Nash equilibrium is in the domain of an isomorphism and not in the domain of an arrow otherwise. If additionally the preference relations are strict then the terminal object (if it exists) of this subcategory is equivalent to the unique Nash equilibrium in pure strategies. I use the homesets of this subcategory to obtain a simple function that attains its maximum in Nash equilbrium. JEL-Classifications: C70, C72.
منابع مشابه
Nash Equilibria, the Price of Anarchy and the Fully Mixed Nash Equilibrium Conjecture
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